Here's what I've sketched. I guarantee nothing. Most of the sketches are "mid sagittal sections" with some ghosts of things that are out of that plane.
In general, I think that the overall height of the carriage needs to be reduced to something just barely tall enough to contain the nut and sear bar. This will allow more wood to be added to the tiller, and that will let us bring the bow binding hole up a bit. Removing material from the carriage should not be a problem because the iron binding is carying the load. There just has to be enough wood to bed the bearing blocks.
The important thing about the mechanism is this. The lengthwise travel of the spanning bar pivot determines the distance that the carriage will travel. That has to be equal to the intended "power stroke" of the bow.
The iron bindings of the carriage are primarily in tension from the rear pivot to the forward bearing block of the nut,so they do not have to be very thick. By contrast, the spanning bar is always in compression, so it must be thick enough not to buckle. Pursuant to that, the articulation of each end of the bar must not permit any twisting or deflection. To that end, the fit with the iron straps of the carriage must be accurate, and that goes for the mortise in the wooden lever as well. The pivots must be large enough in diameter to bear the shear load imposed by the spanning bar. Likewise, there must be enough wood around the forward pivot to support the load. The artist has shown the forward pivot within an area of horn inlay, and that's probably a good idea.
The MS drawing seems to show the hinge held on by clinched nails. That's one of those details that lends a lot of verisimilitude to the drawing. The artist has not shown them on the lever side of the hinge, but they have to be there as well. The pivot of the tickler will end up near those nails, so that is a thing to plan around.
There must be a channel in the bottom of the carriage to allow the "post" of the ticker to enter while the carriage is back.
I have not considered where the tickler return spring will be. Nor have I considered how the tickler's travel is limited.
I have not considered the nature of the catch at the end of the tiller. There must be a sliding member and it must have a spring.
This is, of course, just for starters. There is a lot to think about here.